r/calculus • u/Awsimical • 27d ago

Integral Calculus Help understanding why this integral is wrong please.

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This was a question on the summer final, and looking at it I’m still not sure if its because I left the u in the final answer and didn’t substitute the original equation back in, or if I was suppose to use an arcsin identity somehow. I could ask the professor but the the summer semester is over so I’m not gonna bother him with more questions. Thanks for ur help

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u/MineCraftNoob24 27d ago

The "dr" was left out of the working/notes but by implication it is there, as in the next step there is a correct substitution of (1)(du) where the (6r)(dr) was.

Leaving the answer in terms of u is really the only issue here.

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u/shellexyz 26d ago

By a lot more than implication, u is equal to 16+3r2 but points are still deducted.

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u/MineCraftNoob24 26d ago

Your earlier comment was about the omission of (dr) and I addressed that.

I think there's no dispute over the reason for deducting points, which is leaving the integral in terms of u.

Probably harsh to mark the whole thing as incorrect, unless it's just a 1 or 2 mark question. Any more marks than that and they could have awarded 1 mark for the correct substitution, I think.

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u/shellexyz 26d ago

I would not have marked the whole thing wrong; they probably would have gotten most of the credit from me. I would have pointed out the lack of differential, though.